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Unformatted text preview: through the two observations can be very di/erent from the true slope coe¢ cient when X j and X i are close. Because X 1 and X 2 are closer than X 2 and X 3 in this example, the maximum variance results when we choose i = 1 and j = 2 . Because the distance between X j and X i is the largest when we choose X 1 and X 3 , the minimum variance results when we choose i = 1 and j = 3 . (h) The OLS estimator in (b) has the minimum variance. 1 (i) Yes. The GaussMarkov Theorem states that the OLS estimator is the BLUE. Because the twopoint estimators are linear unbiased estimators, the variance of the OLS estimator must be smaller than or equal to the variance of the any twopoint estimator. 2...
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 Fall '07
 OGAKI
 Econometrics, Variance, Probability theory, Bias of an estimator, Gauss–Markov theorem

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